In past articles, we have covered the concept of harmonics, which are usually defined as frequencies that are integer multiples of the fundamental frequency. When these harmonic frequencies are summed together with the fundamental power frequency (50 or 60Hz normally), the result is a distorted voltage and/or current waveform, no longer the pure sine wave that originated back at the generator. But numerous people have asked why are just the harmonic frequencies present, such as 180Hz, 240Hz, 300Hz, and so on? How does the electronic equipment know to generate only those frequencies? What’s wrong with 178Hz or 316Hz?

Waveforms that contain those frequencies can exist in electrical distribution systems, though they aren’t that common. They are called “interharmonics,” or frequencies between the harmonic frequencies. A special category of those interharmonic frequencies are the subharmonics, which are frequencies below the fundamental frequency. These are more common, and are often the source of the voltage fluctuations that result in light flicker. Subharmonics can also be produced as the result of the interaction between harmonic and interharmonic frequencies. For example, 180Hz and 185Hz signals together would result in a 5Hz signal that falls in the subharmonic region.

But back to the origin of the harmonics: one common cause of harmonic currents is the commutation period of the rectifier-based front-ends of adjustable speed drives and other types of equipment that convert three-phase AC to DC. In the case of ASDs, the DC is then converted back to AC at a different frequency from the original power frequency. This frequency varies depending on the load requirements, but has no appreciable effect on the harmonic content of the current back at the front end.

Since there is a pair of rectifiers (one for positive half cycle of sine wave, one for negative half cycle) for each of the three phases, this is referred to as a six-pulse or six-pole converter. When the control circuitry of the converter turns off one SCR (or thyristor or whatever type of rectifier is used) and turns on the other, there is an overlap period where both devices are turned on. This is because such devices don’t really stop the current flow until the current waveform goes to zero.

Having two devices turned on at once is effectively a short circuit between the phases, which results in a very large current flow for a very short time, until the first device goes off completely. This is the commutation period, and is a synchronous process to the power frequency. As you can see in Figure 1, these notches occur six times in each power frequency cycle. The “rule” on the resulting harmonic currents is H = n x p +/-1, where “n” is integers 1, 2, 3, etc., and “p” is the number of poles (six, in this case). Hence, the dominate harmonics would be 5, 7, 11, 13, 17, 19, and so on.

Another common source of harmonics are single-phase rectified loads, such as found in the front end of most electronic equipment from PCs to TVs to DVD players. The power supply circuitry in these units only conducts current during a period near the peak of the voltage waveform. The width of the pulse is dependent on how much current that the load needs. The more current, the wider the pulse; the less current, the narrower the pulse.

This pulsed waveform happens over and over again each cycle, though over time its width may vary. The mathematical theories regarding such waveforms state that they can be created from the summation of the fundamental frequency waveform along with a series of waveforms that have a weighting or scaling factor applied to their amplitude and have frequencies that are two times the fundamental frequency, three times the fundamental, and so on. This is the same definition as a harmonic. As shown in Figures 2 and 3, if you take the fundamental (60Hz) at a factor of 1, the third harmonic (180Hz) at 0.94, fifth harmonic at 0.78, seventh at 0.58, ninth at 0.36, and so on, and combine all of those signals, you would end up with the waveform in Figure 3.

What about the even-numbered harmonics? So far, all of them that we have considered have been the odd numbers. Even numbered harmonics are not normally found in electrical systems, unless there is current drawn on only one half of the sine wave. This can be from half wave rectifiers that only work on half the cycle, or from full wave rectifiers with something broken so that only half of the rectifiers are working. Waveforms with even harmonics are usually visually detectable because they will lose the symmetry in the waveform, where the one half doesn’t look like a mirror of the other half.

Non-harmonic frequencies can exist in the electrical distribution system, but they are far less common than the harmonic ones. An electrical motor driving a power train with a 27:1 gear ratio can show non-harmonic frequencies. The effects of the electrical current jumping between the scrap metal as it is melted in an electrical arc furnace will have a multitude of frequencies, including interharmonics and subharmonics, and frequencies that only exist for a burst of time, rather than steady state.

But the way that electrical power is used in most equipment today is much more likely to result in odd harmonic currents, which in turn result in harmonic voltages. And data taken over the past 10 years shows that this continues to become more prevalent, grabbing the attention of the standards committees who are looking at what the limits should be before it results in widespread problems. EC

BINGHAM, a contributing editor for power quality, can be reached at 732.287.3680.